Do simulated fishers dream of electric fish

Research Questions

• To NGOs:
  • Flight simulator
• To academics:
  • Heuristics zoo
• To other ABM practitioners:
  • Contribute to general problems

Fisheries

• Applied problem
• Challenges:
  • Spatial
  • Feedbacks
  • Heterogeneity
  • Deep uncertainty
  • Individual-based data
• Where social science goes to die

Where Social Science goes to die - part 1

• Simplest possible fishery: \[ B_{t+1} = B_{t} + f(B_t) - C_t \]
• For any \(C\) there is a \(B\) equilibrium
• Fit by assuming every observation is an equilibrium

• “Their use [equilibrium assumptions] in the past undoubtedly contributed to a number of major fishery collapses.” Haddon (2011)

Where Social Science goes to die - part 2

• The profit maximizing boat; decides:
  • Where to fish
  • Optimal path
  • Number of trips per season
• State space is immense:
  • Belief state of biomass available per fishing spot, per species, per time step
  • Location and action of all competitors
• Bellman equation unsolvable

Metaphysical Dualism

• What does computational tractability tells us about the real world?

• “If your laptop can’t find it, then neither can the market.”

• Pool player analogy
  • Church-Turing thesis

Two solutions in fisheries economics

1. Ignore dynamics
   • Discrete choice models
   • Add indicators to correct for dynamics

   • “this is akin to postponing opening a gift in the knowledge that the joy of consumption will be greater for the wait” Baerenklau (2005)

Two solutions in fisheries economics

2. Ignore fisheries:
   • Assume no space
   • Assume perfect knowledge
   • Assume fishing doesn’t kill of fish
   • Assume one boat

Pragmatism

• Logbook data
• Surveys
  • “I have only 5 spots and cycle through them”
  • “If in a bind, track highliner on radar and copy them”
  • “Explore a fixed proportion of tows”
  • “Draw peaks and valleys on maps”
• Flexibility and Lucas critique

Zoo approach

• Collect decision algorithms
  • From interviews
  • From CS-literature
• Implement them in the same agent-based model
  • Test strengths/weaknesses in theory
  • Compare to real data
• Use it for policy suggestions and sensitivity analysis

The One Agent Problem

The One Agent Problem

• Find the most profitable spot to fish
• Constraints:
  • No biomass information
  • No model knowledge
  • Environment changes over time
• Subproblems:
  • How to explore
  • Explore-Exploit Tradeoff

Explore or Exploit ?

Explore or Exploit ?

Explore-Exploit

• Stochastically choose to explore next trip with probability \(p\)
• Explore in the neighborhood of where you currently go

One Agent world

One Agent sample run

Scaling issues

Scaling issues

Scaling issues

L’enfer, c’est les autres

• Other boats consume biomass
• You can use other boats information
• How to imitate?
• With probability \(p\) explore, otherwise copy somebody who’s doing better

Explore-Exploit-Imitate

\begin{algorithm}
        \caption{Explore-Exploit-Imitate}
        \begin{algorithmic}
\WHILE{game is not over}
  \IF{$\text{random} < \epsilon$}
  \COMMENT{with probability $\epsilon$, explore}
  \STATE $\hat \delta \sim U[-\delta,\delta]$
  \STATE $\text{position} \leftarrow \text{position} + \hat \delta$
  \COMMENT{explore by shocking your position by $\delta$}
  \ELSE
  \STATE $\text{profits}_f$ are the profits made by your most profitable friend
  \STATE $\text{profits}_{\text{me}}$ are the profits just made by this agent
  \IF{$\text{profits}_f>\text{profits}_{\text{me}}$}
     \STATE copy friend location
  \ELSE
    \STATE stay at current location
  \ENDIF
  \ENDIF
\ENDWHILE
        \end{algorithmic}
        \end{algorithm}

Two Agents sample run

Many Agents

Cui prodest?

• Model free
• Adaptive

Oil Prices

Fish the Line (part 1)

Fish the Line (part 2)

Optimization

Gravitational Search

\begin{algorithm}
        \caption{Gravitational Search implementation}
        \begin{algorithmic}
  \STATE $\text{velocity} \leftarrow \text{velocity}_0$
\WHILE{game is not over}
  \FOR{$\text{player}=0$ to $N$}
     \COMMENT{turn all other players' rewards into masses}
     \STATE $\text{mass[player]}\leftarrow \frac{\text{profits[player]}-\min(\text{profits})}{\max(\text{profits})-\min(\text{profits})}$
     \COMMENT{peek at everyone's profits and normalize them}
  \ENDFOR        
  \STATE select the top $Z$ masses
  \STATE $\text{acceleration} \leftarrow 0$
  \FORALL{$i$ such that $\text{masses[i]}$ is one of the top $Z$ masses}
    \STATE $\text{acceleration} \leftarrow \text{acceleration} + G * \frac{\text{masses[here]}*\text{masses[i]}} {\text{distance(here,i))}}$
    \COMMENT{selective gravitational pull}
  \ENDFOR   
  \STATE $\epsilon \sim U[0,1]$
  \COMMENT{Draw random inertia}
  \STATE $\text{velocity} \leftarrow \epsilon \cdot\text{velocity} + \text{accelleration}$
  \STATE $\text{position} = \text{position} + \text{velocity}$
  \STATE play position
\ENDWHILE    

        \end{algorithmic}
        \end{algorithm}

Gravitational Search - Demo

Kernel Regression

Kernel Regression - Demo

Which algorithm performs best in which scenarios?

Which algorithm performs best in which scenarios -pt 2

Which algorithm performs best in real scenarios

Estimating Models!

• Complicated model depends on parameter vector \(\theta\)
• All model estimation strategies do:
  1. Pick some summaries of data \(X\) \[ S = S_1(X), \dots, S_n(X) \]
  2. Generate similar summaries from model: \[ \hat S(\theta) = S_1(\theta),\dots, S_n(\theta) \]
  3. Minimize weighted distance: \[ \theta^* = \arg \min_{\theta} \left( S-\hat S (\theta) \right)^T W \left( S-\hat S (\theta) \right) \]
• In economics one often assumes:
  • Ergodicity
  • 1 to 1 mapping
  • \(\Rightarrow\) consistency!

Issues

\[ \theta^* = \arg \min_{\theta} \left( S-\hat S (\theta) \right)^T W \left( S-\hat S (\theta) \right) \]

• How to minimize?
  • ABC
  • BACCO (GP)
  • Simulated Annealing
• Which summary statistics?
  • 4 to 1? (Altonji,Smith and Vidangos 2013)
  • Computational Costs? Collinearities?
• Which weight?
  • In theory \(W \to \Omega^{-1}\)
  • In practice that is almost never better

Solution?

\[ \theta^* = \arg \min_{\theta} \left( S-\hat S (\theta) \right)^T W \left( S-\hat S (\theta) \right) \]

• Just a complicated mapping \(S \to \theta\)
• Discover it directly by regression
  • Run the model many times, for different \(\hat \theta\), generate \(\hat S(\theta)\)
  • Regress, possibly non-linearly (element-wise) $S $
  • Use regression directly to estimate parameters

RBC model example

RBC model results

RBC model example - cross-correlations

Cross-Correlations results

Advantages

• Select summary statistics, weights and minimizes all at once
• Output is understandable
• Easy to test
• Easy to add uncertainty about other parameters